2012322126On discriminativity of vertex-degree-based indices22A recently published paper [T. Došlić, this journal 3 (2012) 25-34] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertex-degree-based molecular structure descriptors that are being studied in contemporary mathematical chemistry. We also show that these results are straightforwardly obtained by using some identities, well known in the theory of benzenoid hydrocarbons.1-95101--I.GUTMANUniversity of Kragujevac, Kragujevac, SerbiaUniversity of Kragujevac, Kragujevac, SerbiaI R IranZagreb indexVertex-degree-based indicesBenzenoid graphCatacondensed benzenoid graphComputational and electrochemical studies on the redox reaction of 2-(2,3-dihydroxy phenyl)-1,3- dithiane in aqueous solution22Electrode potential of 2-(2,3-dihydroxy phenyl)-1,3-dithiane (DPD) was investigated by means of cyclic voltammetry (CV) at various potential scan rates. The calculated value was compared with the experimental value obtained by cyclic voltammetry (CV). All experiments were done in aqueous phosphate buffer solutions at different pHs. The experimental redox potential of DPD was obtained to be 0.753 V versus SHE (Standard Hydrogen Electrode). DFT-B3LYP calculations using 6-311++G** basis set were performed to calculate the absolute redox potential of DPD. The calculated value of the redox potential relative to SHE is 0.766 V which is in good agreement with the experimental value (0.753).1-103112--M.MAZLOUM-ARDAKANIYazd University, I.R. IranYazd University, I.R. IranI R Iran--H.BEITOLLAHIYazd University, I.R. IranYazd University, I.R. IranI R Iran--H.FARROKHPOURIsfahan University of Technology, IranIsfahan University of Technology, IranI R Iran--A.KHOSHROOIsfahan University of Technology, IranIsfahan University of Technology, IranI R Iranredox reactionDensity functional theoryComputational chemistryCyclic voltammetryOn the tutte polynomial of benzenoid chains22The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.1-113119--G.FATH-TABARUniversity of Kashan,
I. R. IranUniversity of Kashan,
I. R. IranI R Iran--Z.GHOLAM-REZAEIUniversity of Kashan,
I. R. IranUniversity of Kashan,
I. R. IranI R Iran--A.ASHRAFIUniversity of Kashan,
I. R. IranUniversity of Kashan,
I. R. IranI R IranBenzenoid chainTutte polynomialgraphComputing Wiener and hyper–Wiener indices of unitary Cayley graphs22The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.1-121125--A.LOGHMANPayame Noor Universtiy, IRANPayame Noor Universtiy, IRANI R IranUnitary Cayley graphsWiener indexhyper-Wiener indexChromatic polynomials of some nanostars22Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most  colours, which is for a fixed graph G , a polynomial in  , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.1-127135--S.ALIKHANIYazd University, IranYazd University, IranI R Iran--M.IRANMANESHYazd University, Yazd, IranYazd University, Yazd, IranI R IranChromatic polynomialNanostargraphNote on multiple Zagreb indices22The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.1-137143--M.GHORBANIShahid Rajaee Teacher Training
University, I. R. IranShahid Rajaee Teacher Training
University,I R Iran--N.AZIMIShahid Rajaee Teacher Training
University, I. R. Iran;Shahid Rajaee Teacher Training
University,I R IranZagreb indicesVertex degreeMultiple Zagreb indicesOn multiplicative Zagreb indices of graphs22Todeschini et al. have recently suggested to consider multiplicative variants of additive graph invariants, which applied to the Zagreb indices would lead to the multiplicative Zagreb indices of a graph G, denoted by ( ) 1  G and ( ) 2  G , under the name first and second multiplicative Zagreb index, respectively. These are define as     ( ) 2 1 ( ) ( ) v V G G G d v and ( ) ( ) ( ) ( ) 2 G d v d v G uv E G  G    , where dG(v) is the degree of the vertex v. In this paper we compute these indices for link and splice of graphs. In continuation, with use these graph operations, we compute the first and the second multiplicative Zagreb indices for a class of dendrimers.1-145154--A.IRANMANESHTarbiatModares University,
IranTarbiatModares University,
IranI R Iran--M.HOSSEINZADEHTarbiatModares University,
IranTarbiatModares University,
IranI R Iran--I.GUTMANUniversity of Kragujevac, Kragujevac, SerbiaUniversity of Kragujevac, Kragujevac, SerbiaI R IranMultiplicative Zagreb indicesSpliceLinkChain graphsDendrimerFourth order and fourth sum connectivity indices of tetrathiafulvalene dendrimers22The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this paper, the 4-order connectivity and 4-sum connectivity indices of tetrathiafulvalene dendrimers are computed.1-155163--R.HASNIUniversiti Malaysia
Terengganu, Terengganu, MalaysiaUniversiti Malaysia
Terengganu, Terengganu,Malaysia--N.ARIFUniversiti Sains Malaysia,
MalaysiaUniversiti Sains Malaysia,
MalaysiaMalaysia4-Order connectivity index4-Sum connectivity indexDendrimergraphWiener, Szeged and vertex PI indices of regular tessellations22A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate this method to all classes of regular tessellations. In addition, we obtain the vertex Szeged and vertex PI indices of regular tessellations.1-165183--P.MANUELKuwait University, Safat, KuwaitKuwait University, Safat, KuwaitKuwait--I.RAJASINGHDepartment of Mathematics, Loyola College, Chennai 600 034, IndiaDepartment of Mathematics, Loyola College,India--M.AROCKIARAJLoyola College, IndiaLoyola College, IndiaIndiaWiener indexSzeged indexPI indexEmbeddingCongestionRegular plane tessellationsA zero one programming model for RNA structures with arclength ≥ 422In this paper, we consider RNA structures with arc-length 4 . First, we represent these structures as matrix models and zero-one linearprogramming problems. Then, we obtain an optimal solution for this problemusing an implicit enumeration method. The optimal solution corresponds toan RNA structure with the maximum number of hydrogen bonds.1-185193--G.SHIRDELUniversity of Qom, IranUniversity of Qom, IranI R Iran--N.KAHKESHANIUniversity of Qom, IranUniversity of Qom, IranI R IranRNA structureZero-one linear programming problemAdditive algorithmFourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry22The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme and analyze the solvability, stability and convergence of proposed scheme using the Fourier method. The convergence order of method is O(t + n4). Numerical examples demonstrate the theoretical results and high accuracy of proposed scheme.1-195220--M.ABBASZADEUniversity of Kashan, Kashan, I. R. IranUniversity of Kashan, Kashan, I. R. IranI R Iran--M.MOHEBBIUniversity of Kashan, Kashan, I. R. IranUniversity of Kashan, Kashan, I. R. IranI R Irana_ mohebbi@kashanu.ac.irElectroanalytical chemistryReaction-sub-diffusionCompact finite differenceFourier analysissolvabilityunconditional stabilityConvergence